Mark S.
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 1d comment Measure of Connectivity on a Chessboard There are lots of different sorts of functions that might be relevant, depending on what properties you'd like it to satisfy. For example, the number of pieces that must be placed for each player to win might be useful, but if a player has more winning options you might want to weight your function based on that. Or maybe something more detailed about exactly how "far ahead" a player is in this simplified version would be appropriate. Unfortunately, Hex and related games like this are PSPACE complete, so you can't really make the board bigger and get exact data. 1d comment Schröder-Bernstein theorem and injective maps If you take $g(x)=x$ then neither is injective (your example would be more striking), but Schröder-Bernstein would still give you that some bijection exists. 1d comment Are there theoretical applications of trigonometry? Since Conan only has "extremely limited" knowledge of calculus, I think a proof that only uses a single limit at the end would be more appropriate than the proofs in that PDF: en.wikipedia.org/wiki/Basel_problem#A_rigorous_elementary_proof 1d comment Did Feynman mentally compute $\sqrt[3]{1729.03}$ by linear approximation? $1.03/3\approx.34333\approx.34332$ $.34332/144=.05722/24=.02861/12\approx.002384$. Apr 29 comment BEDMAS where the order of Addition before Subtraction matters? @Drakes it's correct because mathematicians chose that convention. This is not something you can prove mathematically, but perhaps empirically by pointing to books/websites that clarify the "same priority, left to right" aspect of the standard order of operations. Apr 25 comment Why Are Some Sets Not Measurable? As I mentioned, there are translation-invariant measures other than the zero measure that cause no problem here: for example, the counting measure. If by non-trivial you mean something equivalent to "assigns a finite positive measure to the unit cube", then if your $\sigma$-algebra contains all the Borel sets then a translation-invariant measure is forced to be a multiple of the Lebesgue measure. Thus, I would say that this really is about the Lebesgue measure, both because that's the most likely context in the textbook, and because the Lebesgue measure is the only interesting case. Apr 24 comment Why Are Some Sets Not Measurable? Yes, they're implicitly talking about the Lebesgue measure: assuming the axiom of choice, not every set can be Lebesgue measurable. Some less useful measures can be defined on the $\sigma$-algebra of all sets, like the one that's $0$ for every set, or the one that's $\infty$ for every nonempty set, or the "counting measure" that gives the size of finite sets and $\infty$ otherwise. Apr 24 comment Why Are Some Sets Not Measurable? $m(B)$ is decidedly not supposed to be zero. A ball of positive radius has positive volume. Apr 22 comment Solving the Gobblet game The rules you linked say there are 24 pieces total, are there actually 32 in the version you're considering? Apr 21 comment Sinusoidal function from $4$ knowns then pick whichever single formula is easiest for you to find. You can get an answer by starting with sine or cosine, and assuming that the coefficient of the trig function $a$ is positive or negative. Try manipulating the variables in my other comment to see if you can adjust the locations of the trough and peak to be what you want, and edit your question with your attempts/observations if you don't get all the way there. Apr 20 comment Sinusoidal function from $4$ knowns Because of what you noted about sine and cosine, it could be either. $a*\cos(bx+c)+d$ is the same bunch of functions as $a*\sin (bx+c)+d$ Apr 20 comment Sinusoidal function from $4$ knowns The period can't be 2 if it goes from min to max in 2 units. Apr 20 comment Index set of dyadic partition Have you been able to make any observations/notice any patterns? Apr 18 comment A Combinatorial Game: the Snake and the Hunter Here is a source for the problem: colombiaaprendiendo.edu.co/eventos/gathering-for-gardner-10 Apr 18 comment Define Grundy values @RossMillikan, good catch! I was following a formal definition closely without thinking. The argument "since B can only move to [something which can move to zero], its value must be zero" does work in general. Apr 17 comment Counterexample to $V=Range(A)\oplus Nullspace(A)$ @Ryles2014 In that example, there is no internal direct sum, so the direct sum in the isomorphism is external. I'm having trouble finding a great source explaining just this distinction, but the first page of mathdoctorbob.org/LinearReview3.pdf only has a little extra stuff. Apr 17 comment Pictures of curves over finite fields with many points Incidentally, it looks like manypoints is down now, but you can get a lot of info from web.archive.org/web/20160324153533/http://manypoints.org/… and perhaps contact one of the moderators listed at web.archive.org/web/20160324063313/http://manypoints.org/… Apr 17 comment Pictures of curves over finite fields with many points I'm not sure what sorts of pictures you'd like. Certainly, the solutions could be plotted as a cloud of points (easiest when the field has prime size), but it seems the famous Klein quartic pictures/graphs are more closely related to the corresponding Riemann eurface, not the solutions over a finite field. Are you asking something like "can we take these equations which have many finite field solutions and look at corresponding Riemann surfaces?" or something more like "can we take these equations, one of which yields a nice Riemann surface, and just look at their finite field solutions?"? Apr 17 comment Tutorials for Sprague-Grundy Theorem/Nimbers? The page is long gone, but you can see there were some problems there at web.archive.org/web/20120322195729/http://www.mathalon.in/… and the first of which was referenced in math.stackexchange.com/questions/20989/finding-four-numbers Apr 17 comment Giving a specific example of a positive sequence increasing to 1 and with its partial products having a positive limit @Nobody For future reference, if you use "@", you can ping a user with a comment. Otherwise only the person who made the post you are commenting will be pinged. See the following for more details: meta.stackexchange.com/questions/43019/…